Dutch Princess Ariane is carried by the sister of Queen Maxima to her baptism ceremony in the Kloosterkerk in The Hague on October 20, 2007.
The royal house said that the Queen is "very shocked and very sad" by the news.
She was also godmother to Queen Maxima's 11-year-old daughter Princess Ariane and the youngest daughter of Jorge Zorreguieta and María del Carmen Cerruti.
The prosecutor's office confirmed the death of Queen Maxima's younger sister, "with no foul play suspected so far", the judicial authority stated on its website. She was 33 years old.
Zorreguieta's body was found in her flat in Buenos Aires, the Argentinian news agency Telam reported.
Local media said Ms Zorreguieta, a psychologist, had struggled with depression. Our thoughts and prayers are with the Queen and her family. A Dutch government spokesperson told Dutch NOS TV that her death appeared to be suicide. "I wish them all the strength necessary to carry this frightful loss together and I trust that they will get the peace and space for that". She canceled her upcoming engagements including a state visit to Estonia, Latvia and Lithuania. She had also worked for the social development ministry in Buenos Aires province and at a United Nations office in Panama.
Her father, Jorge Horacio Zorreguieta, who served as agriculture minister during Argentina's brutal military dictatorship, died previous year in Buenos Aires aged 89.
Argentina's Foreign Minister Jorge Faurie expressed his condolences to Queen Maxima on behalf of Argentina.